The radii of the ends of a frustum of a right circular

Question:

The radii of the ends of a frustum of a right circular cone are 5 metres and 8 metres and its lateral height is 5 metres. Find the lateral surface and volume of the frustum.

Solution:

Lateral surface area of frustum

$=\pi(\mathbf{r}+\mathbf{R}) \mathbf{l}$

 

$=\pi(5+8) \times 5$

$=204.28 \mathrm{~m}^{2}$

Height of cone

$h=\sqrt{5^{2}-(R-r)^{2}}$

$=\sqrt{5^{2}-(8-5)^{2}}$

 

$=\sqrt{13}$

Volume $=\frac{\pi \times \sqrt{13}}{3}\left(8^{2}+5^{2}+40\right)=540.56 \mathrm{~cm}^{3}$

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